Abstract
The growing importance of online social networks where people share information with others leads to the emergence of viral marketing, a new way to promote the sales of products. A derivation of classical Influence Maximization (IM) problem is the Profit Maximization (PM) problem that we focus on in this paper. We propose the PM problem with a cardinality constraint in order to make it closer to the real marketing activities. Without a fixed and pre-determined budget for seed selection, the profit spread metric of PM considers the total benefit and cost. The difference between influence spread metric and profit spread metric is that the latter is no longer monotone and lose the property of submodularity in general. Due to the natural form as the difference between two submodular functions, the profit spread metric admits a DS decomposition. What matters is that we design a Marginal increment-based Prune and Search (MPS) algorithm. From the perspective of marginal increment, MPS algorithm can compute profit spread more directly and accurately. Extensive experiments demonstrate the effectiveness and outperformance of our algorithm.
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Acknowledgements
This is an extended version of a paper (Liman Du et al. 2020) presented in the 9th International Conference on Computational Data and Social Networks (CSoNet 2020). In this version, we redefine the benefit (cost) spread of a node when seed node set is given, propose a theoretical guarantee for MIG algorithm which is used in the second phase of MPS algorithm, and supply more experiments’ result on both synthetic graph and real-world data sets. This research was supported by the National Natural Science Foundation of China under Grant Numbers 12071459 and 11991022.
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Du, L., Chen, S., Gao, S. et al. Nonsubmodular constrained profit maximization from increment perspective. J Comb Optim 44, 2598–2625 (2022). https://doi.org/10.1007/s10878-021-00774-6
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DOI: https://doi.org/10.1007/s10878-021-00774-6